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The purpose of this paper is to report on the flow past a porous square cylinder, implementing the stress jump treatments for the porous‐fluid interface.

The numerical method was developed for flows involving an interface between a homogenous fluid and a porous medium. It is based on the finite volume method with body‐fitted and multi‐block grids. The Brinkman‐Forcheimmer extended model was used to govern the flow in the porous medium region. At its interface, a shear stress jump that includes the inertial effect was imposed, together with a continuity of normal stress.

The present model is validated by comparing with those for the flow around a solid circular cylinder. Results for flow around porous square cylinder are presented with flow configurations for different Darcy number, 10⁻² to 10⁻⁵, porosity from 0.4 to 0.8, and Reynolds number 20 to 250. The flow develops from steady to unsteady periodic vortex shedding state. It was found that the stress jump interface condition can cause flow instability. The first coefficient β has a more noticeable effect whereas the second coefficient β₁ has very small effect, even for Re=200. The effects of the porosity, Darcy number, and Reynolds number on lift and drag coefficients, and the length of circulation zone or shedding period are studied.

The present study implements the numerical method based on finite volume method with a collocated variable arrangement to treat the stress jump condition.

The paper aims to report on the flow past a porous trapezoidal‐cylinder, in which the porous‐fluid interface was treated by implementing the stress jump boundary conditions.

The numerical method was based on the finite‐volume method with body‐fitted and multi‐block grids. The Brinkman‐Forcheimmer extended model was used to govern the flow in the porous medium region. At its interface, a shear stress jump that includes the inertial effect was imposed, together with a continuity of normal stress.

The present model was validated by comparing with those for the flow around a solid circular cylinder. Results for flow around porous expanded trapezoidal cylinder are presented with flow configurations for different Darcy number, 10⁻² to 10⁻⁷, porosity from 0.4 to 0.8, and Reynolds number 20 to 200. The flow develops from steady to unsteady periodic vortex shedding state. The first coefficient β has a more noticeable effect, whereas the second coefficient β₁ has very small effect, even for Re   =   200.

The effects of the porosity, Darcy number and Reynolds number on lift and drag coefficients, and the length of circulation zone or shedding period are studied.

The purpose of this paper is to propose a computational model for thin layers, for problems of linear time-dependent heat conduction. The thin layer is replaced by a zero-thickness interface. The advantage of the new model is that it saves the need to construct and use a fine mesh inside the layer and in regions adjacent to it, and thus leads to a reduction in the computational effort associated with implicit or explicit finite element schemes.

Special asymptotic models have been proposed for linear heat transfer and linear elasticity, to handle thin layers. In these models the thin layer is replaced by an interface with zero thickness, and specific jump conditions are imposed on this interface in order to represent the special effect of the layer. One such asymptotic interface model is the first-order Bövik-Benveniste model. In a paper by Sussmann et al., this model was incorporated in a FE formulation for linear steady-state heat conduction problems, and was shown to yield an accurate and efficient computational scheme. Here, this work is extended to the time-dependent case.

As shown here, and demonstrated by numerical examples, the new model offers a cost-effective way of handling thin layers in linear time-dependent heat conduction problems. The hybrid asymptotic-FE scheme can be used with either implicit or explicit time stepping. Since the formulation can easily be symmetrized by one of several techniques, the lack of self-adjointness of the original formulation does not hinder an accurate and efficient solution.

Most of the literature on asymptotic models for thin layers, replacing the layer by an interface, is analytic in nature. The proposed model is presented in a computational context, fitting naturally into a finite element framework, with both implicit and explicit time stepping, while saving the need for expensive mesh construction inside the layer and in its vicinity.

The purpose of this paper is to develop a counter-extrapolation approach for computational heat and mass transfer with the interfacial discontinuity considered at conjugate interfaces.

By applying finite-difference approximations for the interfacial gradients along the local normal direction, the conjugate system can be simplified to the Dirichlet boundary problems for individual domains. A suitable method for the Dirichlet boundary value condition can then be used. The lattice Boltzmann method has been used to demonstrate the method. The model has been carefully validated by comparing the simulation results and theoretical solutions for steady and unsteady systems with flat or circular interfaces. Furthermore, the cooling process of a hot cylinder in a cold flow, which involves unsteady flow and heat transfer across a curved interface, has been simulated as an example to illustrate the practical usefulness of this model.

Good agreement has been observed in comparisons of simulations and theoretical solutions. The convergence and stability of the method have also been examined and satisfactory results have been obtained. Results of the cylinder cooling process show that a surface insulation layer can effectively reduce the heat transfer process and slow down the cooling process.

This method possesses several technical advantages, including the simple and straightforward algorithm, and accurate representation of the interface geometry. The basic idea and algorithm of the counter-extrapolation procedure presented here can be readily extended to other lattice Boltzmann models and even other computational technologies for heat and mass transfer systems with interface discontinuity.

The purpose of this paper is to present a numerical methodology for the solution of non-Fourier conduction in two-dimensional (2-D) heterogeneous materials with contact resistance.

Energy and heat flux equations with time lagging constant are combined to form a 2-D hyperbolic conduction equation in conservational form, and the resulting equation is solved by finite volume method.

The magnitude of contact resistance is inversely proportional to the temperature jump at the contact surface and phonon transmission coefficient between heterogeneous medium. Numerical results show that higher the contact resistance, lower the heat flux through the interface, lower the strength of transmitted wave and higher the strength of reflected wave at the interface. These results are in agreement with physical expectations. Temperature profiles show expected discontinuity at the interface while the heat fluxes are continuous, demonstrating the accuracy of the proposed methodology.

In most available numerical methods for hyperbolic conduction with contact resistance, contact resistances are treated as internal boundaries at which boundary conditions are specified. In the present formulation, contact resistance between two heterogeneous materials is treated as a part of interface transport properties not as an added boundary condition. This approach makes the formulation much simpler and straightforward for multidimensional applications. This approach is never used previously and is original.

The contact behaviors of droplets on confined surfaces influence significantly their dynamics and morphological transition induced by the electric field. This paper aims to delve into the electric stress, electric field distribution, flow field and evolution of droplet neck to understand the underlying mechanisms.

Electrohydrodynamics of droplets in confined environment is numerically analyzed based on finite volume method (FVM) combining with volume-of-fluid (VOF) method for two-phase interface capturing. Numerical solutions are obtained through solving electrohydrodynamics model coupling fluid dynamics with electrostatics.

It was found that the droplet neck with high interfacial curvature undergoes different transition depending on the contact angle. At large domain height, the droplets on the surfaces with the contact angle of θ < 90° tend to break up into smaller droplets adhered on top and bottom surfaces. The detachment of droplets is identified when the contact angle is much greater than 90°. Notably, the droplets at θ = 90° exhibit asymmetrical shape evolution, but for other cases there is symmetrical shape of droplets during transition process. With decreasing the domain height, no obvious deformation through driving the contraction of the droplet neck is observed.

It remains unclear how the electric field parallel to the surfaces affects the shape transition and electrohydrodynamics of confined droplets when changing the contact angle. In this paper, the authors study the electrohydrodynamics of droplets in confined space when the electric field is exerted parallel to contact surfaces. In particular, the authors consider the effect of the surface wettability on the droplet deformation. The problem is solved through FVM combining with the VOF method to implement the capturing of two-phase interfaces. The results indicate that the electrohydrodynamic behaviors of droplets are sensitive to the contact properties of droplets on the surfaces, which has not been reported in previous works.

External natural convection is rarely studied by numerical simulation in the literature due to the fact that flow of interest takes place in an unbounded domain and that if a limited computational domain is used the corresponding outer boundary conditions are unknown. In this study, we propose outer boundary conditions for a limited computational domain and make the corresponding numerical implementation in the scope of a projection method combining spectral methods and domain decomposition techniques. Numerical simulations are performed for both steady natural convection about an isothermal cylinder and transient natural convection around a line‐source. An experiment is also realized in water using particle image velocimetry and thermocouples to make a comparison during transients of external natural convection around a platinum wire heated by Joule effect. Good agreement, observed between numerical simulations and experiments, validated the outer boundary conditions proposed and their numerical implementation. It is also shown that, if one tolerates prediction error, numerical results obtained remain at least reasonable in a region near the line‐source during the entire transients. We thus paved the way for numerical simulation of external natural convection although further studies remain to be done for higher heating power (higher Rayleigh number).

The purpose of this paper is to experimentally and numerically investigate the interference characteristics between two ski-jump jets on the flip bucket in a large dam spillway when two floodgates are running.

The volume of fluid (VOF) method together with the Realizable k-ε turbulence model were used to predict the flow in two ski-jump jets and the free surface motion in a large dam spillway. The movements of the two gates were simulated using a dynamic mesh controlled by a User Defined Function (UDF). The simulations were run using the prototype dam as the field test to minimize errors due to scale effects. The simulation results are compared with field test observations.

The transient flow calculations, accurately predict the two gate discharges compared to field data with the predicted ski-jump jet interference flow pattern similar to the observed shapes. The transient simulations indicate that the main reason for the deflected nappe is the larger opening difference between the two gates as the buttress side gate closes. When both gates are running, the two ski-jump jets interfere in the flip bucket and raise the jet nappe to near the buttress to form a secondary flow on this jet nappe surface. As the gate continues to close, the nappe surface continues to rise and the surface secondary flow become stronger, which deflects the nappe over the side buttress.

A dynamic mesh is used to simulate the transient flow behavior of two prototype running gates. The transient flow simulation clarifies the hydraulics mechanism for how the two ski-jump jets interfere and deflect the nappe.

Presents a physical model for determining the effective thermal conductivity of a two‐phase composite medium with fixed or moving interfaces. A rigorous numerical method for removing oscillations in the thermal field is proposed. The methodology is based on the volume averaging technique with the assumption that the phases may coexist at a temperature different from that of fusion. The analysis reveals that the effective conductivity of a two‐phase medium is dependent on the phase volume fractions, on their thermal conductivities and on a constitutive constant which determines the geometric structure of the medium and the nature of the interface (fixed or moving). The results for the one and two dimensional conduction‐dominated phase change problem show that the oscillations produced by previous fixed‐grid methods are eliminated.

Of particular interest is the ability of the extended finite element method (XFEM) to capture transient solution and motion of phase boundaries without adaptive remeshing or moving-mesh algorithms for a physically nonlinear phase change problem. The paper aims to discuss this issue.

The XFEM is applied to solve nonlinear transient problems with a phase change. Thermal conductivity and volumetric heat capacity are assumed to be dependent on temperature. The nonlinearities in the governing equations make it necessary to employ an effective iterative approach to solve the problem. The Newton-Raphson method is used and the incremental discrete XFEM equations are derived.

The robustness and utility of the method are demonstrated on several one-dimensional benchmark problems.

The novel procedure based on the XFEM is developed to solve physically nonlinear phase change problems.